Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States

Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magneti...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2008
Main Authors: Dorlas, T.C., Skrypnik, W.I.
Format: Article
Language:English
Published: Інститут математики НАН України 2008
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149000
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States / T.C. Dorlas, W.I. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149000
record_format dspace
spelling Dorlas, T.C.
Skrypnik, W.I.
2019-02-19T12:52:08Z
2019-02-19T12:52:08Z
2008
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States / T.C. Dorlas, W.I. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 82B10; 82B20; 82B26
https://nasplib.isofts.kiev.ua/handle/123456789/149000
Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magnetization in a continuous oscillator variable. The proofs use a generalized Peierls argument and two Griffiths inequalities. The class of spin-oscillator Hamiltonians considered manifest maximal ordering in their ground states. The models have relevance for hydrogen-bond ferroelectrics. The simplest of these is proven to have a unique Gibbsian ground state.
This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
spellingShingle Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
Dorlas, T.C.
Skrypnik, W.I.
title_short Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_full Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_fullStr Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_full_unstemmed Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_sort three order parameters in quantum xz spin-oscillator models with gibbsian ground states
author Dorlas, T.C.
Skrypnik, W.I.
author_facet Dorlas, T.C.
Skrypnik, W.I.
publishDate 2008
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magnetization in a continuous oscillator variable. The proofs use a generalized Peierls argument and two Griffiths inequalities. The class of spin-oscillator Hamiltonians considered manifest maximal ordering in their ground states. The models have relevance for hydrogen-bond ferroelectrics. The simplest of these is proven to have a unique Gibbsian ground state.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149000
citation_txt Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States / T.C. Dorlas, W.I. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ.
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AT skrypnikwi threeorderparametersinquantumxzspinoscillatormodelswithgibbsiangroundstates
first_indexed 2025-12-07T17:29:53Z
last_indexed 2025-12-07T17:29:53Z
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